Can I mix use SQL Server backup software Microsoft SQL Server Agent in backing up a database?

No .

If you define backup jobs for the same database in both backup utilities, Microsoft SQL Server does not record the program who create backups. When you plan to restore this database, you will find you are in a complicated situation, such as you may need a full backup created by SQL Server Agent and a differential backup created by SQL Server Backup software. It is strongly recommended that you just select one SQL Server Backup utility to back up your database.